Chapter 15 Statistical Process Control
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Transcript of Chapter 15 Statistical Process Control
1
Chapter 15Statistical ProcessProcess Control
MGS3100Julie Liggett De Jong
Statistical Process Control is used to prevent quality problems
Statistical Process Control ….
How it works.
Take periodic samples from process
2
Take periodic samples from process
Plot sample points on control chart
Determine if process is within limits
Take periodic samples from process
Plot sample points on control chart
Determine if process is within acceptable limits
Variation
1 Common Causes1. Common CausesVariation inherent in a processEliminated through system improvements
Variation
2 Special Causes2. Special CausesVariation due to identifiable factorsModified through operator or management action
3
Attribute measures
ProductProduct characteristic evaluated with a discrete choice:Good / bad Yes / NoPass / Fail
Attribute measures
ProductProduct characteristics evaluated with a discrete choice:Good / bad Yes / NoPass / Fail
Attribute measures
ProductProduct characteristics evaluated with a discrete choice:
Good / bad Yes / NoPass / Fail
Variable measures
Measurable product characteristic:
Length size weightLength, size, weight, height, time, velocity
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Variable measures
Measurable product characteristics:
Length size weightLength, size, weight, height, time, velocity
Variable measures
Measurable product characteristics
Length size weightLength, size, weight, height, time, velocity
SPC Applied to Services
Hospitals
Timeliness
Responsiveness
Accuracy of lab tests
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Grocery Stores
Check-out time
Stocking
Cleanliness
AirlinesLuggage handling Waiting times Courtesy
Fast Food Restaurants
Waiting timesWaiting times
Food quality
Cleanliness
Internet Orders
Order accuracyOrder accuracy Packaging Delivery time Email confirmationconfirmationPackage tracking
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Insurance
Billing accuracy
Timeliness of claims processing
Agent availabilityg y
Response time
Control ChartsControl Charts
Graphs that establish process control limits
Attribute measures:P-ChartsC-Charts
7
Variable measures:Mean (x-bar) control charts Range (R) control charts
A Process is in control if:
A Process is in control if:
No sample points are outside control limits
A Process is in control if:
Most points are near process average
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A Process is in control if:
About equal number of points are above & below centerline
A Process is in control if:
Points appear to be randomly distributed
Process Control Chart
Uppercontrol
li it
Out of control
limit
Processaverage
Lowercontrol
1 2 3 4 5 6 7 8 9 10Sample number
controllimit
Figure 15.1
To develop Control Charts:
Use in-control data
If non-random causes are present, find them and discard data related to them
Correct control chart limits
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Control ChartsControl Charts Measures Description p Chart Attributes Calculates percent defectives
in samplep
r Chart (range chart)
Variables Reflects the amount of dispersion in a sample
x bar Chart (mean chart)
Variables Indicates how sample results relate to the process average
Cp Process Measures the capability of a p (Process Capability
Ratio)
Capability p y
process to meet design specifications
Cpk (Process Capability
Index)
Process Capability
Indicates if the process mean has shifted away from design target
Control ChartsControl Charts Measures Description p Chart Attributes Calculates percent defectives
in samplep
r Chart (range chart)
Variables Reflects the amount of dispersion in a sample
x bar Chart (mean chart)
Variables Indicates how sample results relate to the process average
Cp Process Measures the capability of a p (Process Capability
Ratio)
Capability p y
process to meet design specifications
Cpk (Process Capability
Index)
Process Capability
Indicates if the process mean has shifted away from design target
p-Chart
UCL = p + zσp
LCL = p - zσp
where
p = the sample proportion defective; an estimate of the process average
p
p-Chart
UCL = p + zσp
LCL = p - zσp
where
p = the sample proportion defective; an estimate of the process average
p
p =total defectives
total sample observations
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p-Chart
UCL = p + zσp
LCL = p - zσp
where
p = the sample proportion defective; an estimate of the process average
z = the number of standard deviations from the process average
p
average
The Normal Distribution
μ=0 1σ 2σ 3σ-1σ-2σ-3σ
95%99.74%
Control Chart Z Values
Smaller Z values make more narrow control limits and more sensitive chartsZ = 3.00 is standardCompromise between sensitivity and errors
μ=0 1σ 2σ 3σ-1σ-2σ-3σ
95%99.74%
p-Chart
UCL = p + zσp
LCL = p - zσp
where
p = the sample proportion defective; an estimate of the process average
z = the number of standard deviations from the process average
p
averageσp = the standard deviation of the sample proportion
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p-Chart
UCL = p + zσp
LCL = p - zσp
σp = p(1 - p)
np
p =total defectives
total sample observationsp = total sample observations
p-Chart Example ~Western Jeans Company p337
20 samples of 100 pairs of jeans (n = 100)
NUMBER OF PROPORTION
p-Chart Example ~Western Jeans Company
NUMBER OF PROPORTIONSAMPLE DEFECTIVES DEFECTIVE
1 6 .062 0 .003 4 .04: : :: : :
20 18 .18200
Ex 1, P337
0 16
0.18
0.20
UCL = 0.190
p-Chart Example ~Western Jeans Company
0.08
0.10
0.12
0.14
0.16
Prop
ortio
n de
fect
ive
p = 0.10
0.02
0.04
0.06
P
Sample number2 4 6 8 10 12 14 16 18 20
LCL = 0.010
Ex 1, P337
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Control ChartsControl Charts Measures Description p Chart Attributes Calculates percent defectives in
samplesample
r Chart (range chart)
Variables Reflects the amount of dispersion in a sample
x bar Chart (mean chart)
Variables Indicates how sample results relate to the process average
Cp Process Measures the capability of a p(Process Capability
Ratio)
Capability y
process to meet design specifications
Cpk (Process Capability
Index)
Process Capability
Indicates if the process mean has shifted away from design target
Range ( R ) Chart
UCL = D R LCL = D RUCL = D4R LCL = D3R
R = ∑Rk
where:where:
R = range of each samplek = number of samples
n A2 D3 D4
SAMPLE SIZE FACTOR FOR x-CHART FACTORS FOR R-CHART
2 1.88 0.00 3.273 1.02 0.00 2.574 0 73 0 00 2 28
Factors for R-Chart: D3 & D4
4 0.73 0.00 2.285 0.58 0.00 2.116 0.48 0.00 2.007 0.42 0.08 1.928 0.37 0.14 1.869 0.44 0.18 1.82
10 0.11 0.22 1.7811 0.99 0.26 1.7412 0.77 0.28 1.7213 0.55 0.31 1.6914 0.44 0.33 1.6715 0.22 0.35 1.6516 0.11 0.36 1.6417 0.00 0.38 1.6218 0.99 0.39 1.6119 0.99 0.40 1.6120 0.88 0.41 1.59
Table 1, P343
R-Chart Example ~ Goliath Tool Company (p345)
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R-Chart Example ~ Goliath Tool Company
OBSERVATIONS (SLIP-RING DIAMETER, CM)SAMPLE k 1 2 3 4 5 x RSAMPLE k 1 2 3 4 5 x R
1 5.02 5.01 4.94 4.99 4.96 4.98 0.082 5.01 5.03 5.07 4.95 4.96 5.00 0.123 4.99 5.00 4.93 4.92 4.99 4.97 0.084 5.03 4.91 5.01 4.98 4.89 4.96 0.145 4.95 4.92 5.03 5.05 5.01 4.99 0.136 4.97 5.06 5.06 4.96 5.03 5.01 0.107 5.05 5.01 5.10 4.96 4.99 5.02 0.14
R = max – min = 5.02 – 4.94 = 0.08
8 5.09 5.10 5.00 4.99 5.08 5.05 0.119 5.14 5.10 4.99 5.08 5.09 5.08 0.15
10 5.01 4.98 5.08 5.07 4.99 5.03 0.10total 50.09 1.15
Ex 3, P344
n A2 D3 D4
SAMPLE SIZE FACTOR FOR x-CHART FACTORS FOR R-CHART
2 1.88 0.00 3.273 1.02 0.00 2.574 0 73 0 00 2 28
Factors for R-Chart: D3 & D4
4 0.73 0.00 2.285 0.58 0.00 2.116 0.48 0.00 2.007 0.42 0.08 1.928 0.37 0.14 1.869 0.44 0.18 1.82
10 0.11 0.22 1.7811 0.99 0.26 1.7412 0.77 0.28 1.7213 0.55 0.31 1.6914 0.44 0.33 1.6715 0.22 0.35 1.6516 0.11 0.36 1.6417 0.00 0.38 1.6218 0.99 0.39 1.6119 0.99 0.40 1.6120 0.88 0.41 1.59
Table 1, P343
R-Chart Example ~Goliath Tool Company
UCL = 0.243
ange R = 0.115
0.28 –
0.24 –
0.20 –
0.16 –
Example 15.3
LCL = 0
Ra
Sample number
|1
|2
|3
|4
|5
|6
|7
|8
|9
|10
0.12 –
0.08 –
0.04 –
0 –
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x-Chart Calculations
UCL = x + A2R LCL = x - A2R= =
x = x1 + x2 + ... xk
k=
where
x = the average of the sample meansR bar = the average range values
=
x-Chart Example ~ Goliath Tool Company
OBSERVATIONS (SLIP-RING DIAMETER, CM)SAMPLE k 1 2 3 4 5 x RSAMPLE k 1 2 3 4 5 x R
1 5.02 5.01 4.94 4.99 4.96 4.98 0.082 5.01 5.03 5.07 4.95 4.96 5.00 0.123 4.99 5.00 4.93 4.92 4.99 4.97 0.084 5.03 4.91 5.01 4.98 4.89 4.96 0.145 4.95 4.92 5.03 5.05 5.01 4.99 0.136 4.97 5.06 5.06 4.96 5.03 5.01 0.107 5.05 5.01 5.10 4.96 4.99 5.02 0.14
(5.02 + 5.01 + 4.95 + 4.99 + 4.96)/5 = 4.98
8 5.09 5.10 5.00 4.99 5.08 5.05 0.119 5.14 5.10 4.99 5.08 5.09 5.08 0.15
10 5.01 4.98 5.08 5.07 4.99 5.03 0.10total 50.09 1.15
Ex 4, P345
n A2 D3 D4
SAMPLE SIZE FACTOR FOR x-CHART FACTORS FOR R-CHART
2 1.88 0.00 3.273 1.02 0.00 2.574 0 73 0 00 2 28
Factors for R-Chart: D3 & D4
4 0.73 0.00 2.285 0.58 0.00 2.116 0.48 0.00 2.007 0.42 0.08 1.928 0.37 0.14 1.869 0.44 0.18 1.82
10 0.11 0.22 1.7811 0.99 0.26 1.7412 0.77 0.28 1.7213 0.55 0.31 1.6914 0.44 0.33 1.6715 0.22 0.35 1.6516 0.11 0.36 1.6417 0.00 0.38 1.6218 0.99 0.39 1.6119 0.99 0.40 1.6120 0.88 0.41 1.59
Table 1, P343
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UCL = 5.08
5.10 –
5.08 –
5 06
x-Chart Example ~ Goliath Tool Company
Mea
n
5.06 –
5.04 –
5.02 –
5.00 –
4.98 –
x = 5.01=
Example 15.4
LCL = 4.94
Sample number
|1
|2
|3
|4
|5
|6
|7
|8
|9
|10
4.96 –
4.94 –
4.92 –
Using x- and R-charts together
Each measures the process differently Both process average (x bar chart) and variability (R chart) must be in y ( )control
Sample Size Determination
Attribute control charts (p chart)• 50 to 100 parts in a sample
Sample Size Determination
Variable control charts (R- & x bar- charts)• 2 to 10 parts in a sample
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Process Capability
• Control limits (the “Voice of the Process” or the “Voice of the Data”): based on natural variations (common causes)
• Tolerance limits (the “Voice of the Customer”): customer requirements
Process Capability: A measure of how• Process Capability: A measure of how “capable” the process is to meet customer requirements; compares process limits to tolerance limits
Range of natural variability in process• Measured with control charts.
Process Capability
Process cannot meet specifications if natural variability exceeds tolerances3-sigma quality
• Specifications equal the process control limits.
6 i li6-sigma quality• Specifications twice as large as control
limits
Design Specifications
Process Capability
Design Specifications
(a) Natural variation exceeds design specifications; process is not capable of meeting specifications all the time.
Process
(b) Design specifications and natural variation the same; process is capable of meeting specifications most the time.
Process
Figure 15.5
Design Specifications
Process Capability
(c) Design specifications greater than natural variation; process is capable of always conforming to specifications.
ProcessDesign
Specifications
Figure 15.5
(d) Specifications greater than natural variation, but process off center; capable but some output will not meet upper specification.
Process
17
Process Capability MeasuresProcess Capability Ratio (Cp )
t lCCpp ==
==
tolerance rangeprocess range
upper specification limit -lower specification limit
66σ
Design Specifications
a) Cp < 1.0
Process Capability MeasuresProcess Capability Ratio ( Cp )
Design S ifi i
Process
Design Specifications
Processb) Cp = 1.0
c) Cp > 1.0
Specifications
ProcessFigure 15.5
Computing Cp
Net weight specification = 9.0 oz ± 0.5 ozP 8 80
Munchies Snack Food Company
Process mean = 8.80 ozProcess standard deviation = 0.12 oz
Cp =
upper specification limit -lower specification limit
6σ
= = 1.399.5 - 8.56(0.12)
Ex 6, P 354
Process Capability MeasuresProcess Capability Index ( Cpk )
Cpk = minimum
x - lower specification limit3σ
=
upper specification limit - x3σ
=,
D iDesign Specifications
Process
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C > 1 00: Process is capable of meeting design
Process Capability MeasuresProcess Capability Index ( Cpk )
Cpk > 1.00: Process is capable of meeting design specifications
Cpk < 1.00: Process mean has moved closer to one of the upper or lower design specifications and will generate defects
Cpk = 1.00: The process mean is centered on the design target.
Computing Cpk
Net weight specification = 9.0 oz ± 0.5 ozProcess mean = 8.80 oz
Munchies Snack Food Company
Process standard deviation = 0.12 oz
Cpk = minimum
x - lower specification limit3σ
=
upper specification limit - x=,
= minimum , = 0.83
3σ
8.80 - 8.503(0.12)
9.50 - 8.803(0.12)
Ex 7, P354
The Process Capability Index
Cpk < 1 Not Capablepk p
Cpk > 1 Capable at 3σ
Cpk > 1.33 Capable at 4σ
Cpk > 1.67 Capable at 5σ
Cpk > 2 Capable at 6σ